# GG-13: Bond/Rate Cross-Reference — Conditional Rate Channel

The gravity paper's bilateral rate findings may provide independent support
for the conditional rate channel. Testing whether demographics predict rates
conditional on income/safe-issuer status.

## Z₁ on Rate Levels by Subsample

| DV | Sample | Z₁ | p-value | N | Countries |
|---|---|---|---|---|---|
| 10Y Bond | Full | -13.7 | 0.3861 | 1018 | 23 |
| 10Y Bond | OECD | -13.7 | 0.3861 | 1018 | 23 |
| 10Y Bond | Safe issuers | 13.6 | 0.4156 | 665 | 14 |
| 10Y Bond | Non-safe | -47.1 | 0.1741 | 353 | 9 |
| Real 10Y | Full | 44.0** | 0.0131 | 907 | 23 |
| Real 10Y | OECD | 44.0** | 0.0131 | 907 | 23 |
| Real 10Y | Safe issuers | 48.6*** | 0.0096 | 584 | 14 |
| Real 10Y | Non-safe | 53.1 | 0.1311 | 323 | 9 |
| 3M Rate | Full | -3.8 | 0.8530 | 983 | 23 |
| 3M Rate | OECD | -3.8 | 0.8530 | 983 | 23 |
| 3M Rate | Safe issuers | 15.9 | 0.5256 | 607 | 14 |
| 3M Rate | Non-safe | -46.5 | 0.2377 | 376 | 9 |

## Z₁×Safe-Issuer Interaction on Rates

**10Y Bond**: Z₁(base) = -12.3 (p=0.4462), Z₁×safe = -0.3 (p=0.6484)
**Real 10Y**: Z₁(base) = 44.5** (p=0.0124), Z₁×safe = -0.7 (p=0.4831)
**3M Rate**: Z₁(base) = -12.1 (p=0.5746), Z₁×safe = 0.9 (p=0.2782)

## Pre/Post-GFC Rate Effects

| DV | Period | Z₁ | p-value | N |
|---|---|---|---|---|
| 10Y Bond | Pre-GFC (≤2007) | 34.9* | 0.0653 | 627 |
| 10Y Bond | Post-GFC (≥2009) | -33.4 | 0.2328 | 368 |
| Real 10Y | Pre-GFC (≤2007) | 40.4*** | 0.0060 | 516 |
| Real 10Y | Post-GFC (≥2009) | 26.5 | 0.3996 | 368 |
| 3M Rate | Pre-GFC (≤2007) | 23.6 | 0.3861 | 592 |
| 3M Rate | Post-GFC (≥2009) | -57.9** | 0.0135 | 368 |

## Verdict

The rate channel evidence should be assessed against the gravity paper's bilateral findings:
- If demographics predict rates conditional on safe-issuer status, this supports the Carvalho channel
- If the effect concentrates pre-GFC and among safe issuers, it is consistent with the structural break documented in the monetary paper
- The bilateral gravity paper's fitted-rate mediation (originally 58%) should be re-evaluated in light of the KAOPEN spuriousness — the rate channel may be more important than openness for explaining bilateral flows